Question

1. Find the domain for which the function f(x) =2x2-1 and g(x) =1-3x are equal.

Answer 1

Hey there ☺

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Solution -:


$f \: (x) = g \: (x) \\ {2x}^{2} - 1 = 1 - 3x \\ {2x}^{2} - 3x - 2 = 0 \\ {2x}^{2} + 4x - x - 2 = 0 \\ 2x(x + 2) - 1(x + 2) = 0 \\ (2x - 1)(x + 2) \\ x = \frac{1}{2} \: \: \: \\ x = - 2$
The domain for which the function f(x) = g(x) is (1/2 , -2)


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Hope it helps :)

Answer 2

Given:

Two functions are given:

f(x) = 2x²-1 and g(x) = 1-3x

To Find:

Find the domain for which the function f(x) and g(x) are equal.

Solution:

Finding the domain for which two functions are equal means finding the values of x for which the value of the functions be equal.

So we will find the value of x for which the vale of functions be equal.

value of function at x = f(x) = g(x)

2x²-1 = 1-3x

2x² + 3x -2 =0

2x² + 4x -x -2 = 0

2x(x + 2) -(x+ 2) =0

(2x - 1)(x+2) = 0

x= -2 , 1/2

so the value of x where value of the functions be equal are -2,1/2.

Hence the domain for which the functions are equal is { -2 , 1/2}